Subband coding using local bases in multiple dimensions

Abstract

A method and apparatus for encoding and decoding multi-dimensional signals is disclosed. Non-separable multi-dimensional filters are utilized. Analysis filters encode the signal by applying a windowing function and a reduction function to the multi-dimensional signal. This produces a prototype. The prototype is then replicated as many times as required by utilizing a modulation function. Synthesis filters then decode the encoded signal by utilizing the inverse of the encoding process.

The invention claimed is: 
     
       1. A method of subbanding a multi-dimensional signal, comprising the steps of: utilizing a prototype for defining a plurality of processing regions of a multi-dimensional signal,   reducing information redundancy by substantially eliminating repetitive values in at least a subset of said processing regions of said multi-dimensional signal, and   modulating at least one of said processing regions to a different frequency region, thereby performing subbanding of the multi-dimensional signal.   
     
     
       2. A method of subbanding a multi-dimensional signal as claimed in claim 1 wherein said method of subbanding is performed with at least one non-separable, multi-dimensional filter. 
     
     
       3. A method of subbanding a multi-dimensional signal as claimed in claim 2 wherein said modulation step is performed with a modulation circuit based on a sinusoidal function. 
     
     
       4. A method of subbanding a multi-dimensional signal as claimed in claim 2 wherein said modulation step is performed with a modulation circuit based on a non-sinusoidal function. 
     
     
       5. A method of subbanding a multi-dimensional signal as claimed in claim 1 wherein said method of subbanding is performed with at least one separable filter and said modulation step is performed with a circuit based on a non-sinusoidal function. 
     
     
       6. A method of subbanding a multi-dimensional signal as claimed in claim 2 wherein said prototype is a circuit W, where W is defined by the relationship W=diag(Wij). 
     
     
       7. A method of subbanding a multi-dimensional signal as claimed in claim 2 wherein said reduction step is performed by a circuit implementation of a block diagonal matrix K. 
     
     
       8. A method of subbanding a multi-dimensional signal as claimed in claim 2 wherein said modulating step is performed by a circuit implementation of a modulation matrix G defined by the relationship G -1  *G=I. 
     
     
       9. A method of subbanding a multi-dimensional signal as claimed in claim 2 wherein said method is implemented in an analysis system. 
     
     
       10. A method of reconstructing a multi-dimensional signal subbanded by the method of claim 1 comprising the steps of: demodulating each of said processing regions,   inserting said repetitive values back into each of said processing regions, and   applying a prototype to place said processing regions back in consecutive order, thereby reconstructing said multi-dimensional signal.   
     
     
       11. A method of reconstructing as claimed in claim 10 wherein said method of reconstructing is performed with at least one non-separable, multi-dimensional filter. 
     
     
       12. A method of reconstructing as claimed in claim 10 wherein said demodulation step is performed with a modulation circuit based on the inverse of a sinusoidal function. 
     
     
       13. A method of reconstructing as claimed in claim 10 wherein said demodulation step is performed with a modulation circuit based on the inverse of a non-sinusoidal function. 
     
     
       14. A method of reconstructing as claimed in claim 10 wherein said prototype is a circuit defined by the relationship W -1 , where W -1  is the inverse of a window matrix W. 
     
     
       15. A method of reconstructing as claimed in claim 10 wherein said reduction step is performed by a circuit implementation defined by the relationship K -1 , where K -1  is the inverse of a reduction matrix K. 
     
     
       16. A method of reconstructing as claimed in claim 10 wherein said demodulating step is performed by a circuit defined by G -1 , where G -1  is the inverse of a modulation matrix G. 
     
     
       17. A method of subbanding a multi-dimensional signal as claimed in claim 10 wherein said method is implemented in a synthesis system. 
     
     
       18. A communications system, comprising: an analysis system for processing a multi-dimensional signal, said analysis system including at least one filter, wherein said filter further comprises a prototyping means, a reduction means and a modulation means, for processing said multi-dimensional signal,   a first sampler for sampling said multi-dimensional signal,   a coding means for coding said multi-dimensional signal,   a transmission means for transmitting said multi-dimensional signal,   a decoding means for decoding said multi-dimensional signal,   a second sampler for resampling said multi-dimensional signal, and   a synthesis system for synthesizing said multi-dimensional signal, said synthesis system including at least one filter, wherein said filter further comprises an inverse prototyping means, an inverse reduction means and an inverse modulation means.   
     
     
       19. A communications system as claimed in claim 18 wherein said analysis system is implemented with circuits defined by the relationship Y=H T  *X, where H T  =W*K*G, where W is a window matrix, K is a reduction matrix and G is a modulation matrix. 
     
     
       20. A communications system as claimed in claim 18 wherein said synthesis system is implemented with circuits defined by the relationship X=H -T  Y, H -T  =G -T  *K -T  *W -T , where W is a window matrix, K is a reduction matrix and G is a modulation matrix. 
     
     
       21. A method of subbanding a multi-dimensional signal using a filter characterized by a window matrix, a reduction matrix and a modulation matrix, said method comprising the steps of: parsing through said multi-dimensional signal in accordance with said window matrix, thereby producing a windowed signal,   reducing similarities in said windowed signal in accordance with said reduction matrix, thereby producing a reduced signal, and   modulating said reduced signal in accordance with said modulation matrix, thereby subbanding said multi-dimensional signal.   
     
     
       22. A method of subbanding a multi-dimensional signal as claimed in claim 21 wherein said modulating step is performed with a circuit based on a sinusoidal function. 
     
     
       23. A method of subbanding a multi-dimensional signal as claimed in claim 21 wherein said modulating step is performed with a circuit based on a non-sinusoidal function. 
     
     
       24. A multi-dimensional filter for processing a multi-dimensional signal, said multi-dimensional filter comprising: a prototype for sampling said multi-dimensional signal,   a modulation means for consecutively moving said prototype through said multi-dimensional signal, and   a reduction means, associated with said prototype and said modulation means, for reducing similarities in said multi-dimensional signal.   
     
     
       25. A method of processing a one-dimensional signal comprising the steps of: sampling said one-dimensional signal with a prototype,   reducing any similarities in said one-dimensional signal with a reduction means, and   moving said prototype through said one-dimensional signal with a modulation means based on a non-sinusoidal function.   
     
     
       26. A method of processing a separable multi-dimensional signal, said method comprising the steps of: performing the steps in claim 25 in each dimension of said multi-dimensional signal.   
     
     
       27. A method of designing a multi-dimensional filter for subbanding a multi-dimensional signal, said method comprising the steps of: defining a prototype (W) governed by the relationship W=diag(Wij),   defining a modulator (G) selected from a sample space of functions, for modulating said prototype, wherein said modulator is governed by the relationship G -1  *G=I, and   defining a reduction element (K) wherein said reduction element operates in conjunction with said prototype and said modulator in subbanding said multi-dimensional signal.